Reference no: EM133411981

Question: Jumbo manufacturers bicycles for all ages. The demand forecast for the coming year is shown in the following table. Capacity at Jumbo is limited by the number of employees it hires. Employees are paid $10 per hour for regular time and $15 per hour for overtime. Each bicycle requires two hours of work from one employee. The plant works 20 days a month and eight hours a day of regular time. Overtime is restricted to a maximum of 20 hours per employee per month. Jumbo currently has 250 employees and prefers not to change that number.

Each bicycle uses $35 of material. Carrying a bicycle in inventory from one month to the next costs $4. Jumbo starts with 4,000 bicycles in inventory and wants to end the year with 4,000 bicycles in inventory. Bicycles are currently sold to retailers for $80 each. The market is shared between Jumbo and its competitor, Shrimpy. Jumbo is the process of making its production planning and promotion decisions. Jumbo wants to consider only plans without any stockouts. One option is to drop the sale price by $3 (from $80 to $77) for one month in the year. The outcome of this action by Jumbo is influenced by the action taken by Shrimpy. If neither firm promotes, the forecast demand for Jumbo is shown in the table below. If Jumbo promotes in a given month but Shrimpy does not, Jumbo sees consumption (this does not include forward buying) in that month increase by 40 percent and forward buying of 10 percent from each of the two following months. If Shrimpy promotes in a given month but Jumbo does not, Jumbo sees consumption in the month drop by 40 percent with no change in the other months. If both promote in a given month, neither sees an increase in consumption but both see forward buying of 15 percent from each of the two following months. The debate within Jumbo is whether to promote, and if so, whether to do it in April or June.

For the following questions, assume that Shrimpy and Jumbo have similar demand.

a. What is the optimal production plan for Jumbo assuming no promotion by either Jumbo or Shrimpy? What are the annual profits for Jumbo?

b. What are the profits for Jumbo if Shrimpy promotes in April but Jumbo does not promote throughout the year (it follows everyday low pricing)? What are the profits for Jumbo if it promotes in April but Shrimpy does not promote throughout the year?

Comment on the benefit from promoting versus the loss from not promoting if the competitor does.

c. What are the optimal production plan and profits if both promote in April? Both promote in June? Jumbo promotes in June but Shrimpy in April?

d. What is the best decision for Jumbo if it can coordinate its decision with Shrimpy?

e. What is the best decision for Jumbo if it wants to maximize its minimum profits no matter what Shrimpy does?